New Foundations

It was around the beginning of my undergraduate studies when I became interested in foundations of mathematics in general and axiomatic set theory in particular. Shortly after, I started reading parts of Abraham Fraenkel’s brilliant book Einleitung in die Mengenlehre. I read the second edition of this book, which had originally been published in the 1920ies. In his book, Fraenkel first introduces set theory in a naïve way, then discusses certain paradoxes arising from the naïve treatment, and finally presents the axiomatic set theory developed by Ernst Zermelo and himself.

A few weeks ago, I stumbled across set theory again when Sergei Tupailo gave two talks at the Institute of Cybernetics on an alternative axiomatic set theory called New Foundations. The first talk was about a classical proof by Ernst Specker, the second one was about a contribution by Tupailo himself. Tupailo’s talks caused me to have a look at these “new foundations”, which were, in fact, completely new to me. In this blog post, I want to tell you a bit about this interesting topic. Continue reading